Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Composite quarks and leptons with embedded QCD

Benoît Assi1,2 and Bogdan A. Dobrescu1

Phys. Rev. D 112, 075005 – Published 3 October, 2025

DOI: https://doi.org/10.1103/bns1-b9fy

Abstract

We construct a model of quark and lepton compositeness based on an SU(15) gauge interaction that confines chiral preons, which are also charged under the weakly coupled SU(4)PS×SU(2)L×SU(2)R gauge group. The breaking of the latter, down to the Standard Model group, is achieved by scalar SU(15) bound states at a scale in the 30–100 TeV range. The embedding of the QCD gauge group in SU(4)PS slows down the running of αs in the UV. We estimate the effects of the strongly coupled SU(15) dynamics on the running of the SU(4)PS×SU(2)L×SU(2)R gauge couplings, which likely remain perturbative beyond the compositeness scale of about 103–104  TeV, and even above a unification scale. A composite vectorlike lepton doublet acquires a mass in the TeV range probed at future colliders, and an extended Higgs sector arises from six-preon bound states.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (45)

  1. G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, in Recent Developments in Gauge Theories, NATO Advanced Study Institutes Series Vol. 59 (Springer, Boston, MA, 1980), p. 135.
  2. B. A. Dobrescu, Quark and lepton compositeness: A renormalizable model, Phys. Rev. Lett. 128, 241804 (2022).
  3. J. C. Pati, A. Salam, and J. A. Strathdee, A Preon model with hidden electric and magnetic type charges, Nucl. Phys. B185, 416 (1981).
  4. I. Bars and S. Yankielowicz, Composite quarks and leptons as solutions of anomaly constraints, Phys. Lett. 101B, 159 (1981); I. Bars, Family structure with composite quarks and leptons, 106B, 105 (1981).
  5. C. Q. Geng and R. E. Marshak, Two realistic preon models with SU(N) metacolor satisfying complementarity, Phys. Rev. D 35, 2278 (1987).
  6. B. Assi and B. A. Dobrescu, Proton decay from quark and lepton compositeness, J. High Energy Phys. 12 (2022) 116.
  7. J. C. Pati and A. Salam, Lepton number as the fourth color, Phys. Rev. D 10, 275 (1974); 11, 703(E) (1975).
  8. D. B. Kaplan, Chiral gauge theory at the boundary between topological phases, Phys. Rev. Lett. 132, 141603 (2024); D. B. Kaplan and S. Sen, Weyl fermions on a finite lattice, 132, 141604 (2024); S. Aoki, H. Fukaya, and N. Kan, A lattice formulation of Weyl fermions on a single curved surface, Prog. Theor. Exp. Phys. 2024, 043B05 (2024); M. Golterman and Y. Shamir, Conserved currents in five-dimensional proposals for lattice chiral gauge theories, Phys. Rev. D 109, 114519 (2024); D. B. Kaplan and S. Sen, Regulating chiral gauge theory at θ=0, arXiv:2412.02024.
  9. E. Eichten, K. Kang, and I. G. Koh, Anomaly free complex representations in SU(N), J. Math. Phys. (N.Y.) 23, 2529 (1982).
  10. E. Eichten, R. D. Peccei, J. Preskill, and D. Zeppenfeld, Chiral gauge theories in the 1/N expansion, Nucl. Phys. B268, 161 (1986).
  11. P. B. Smith, A. Karasik, N. Lohitsiri, and D. Tong, On discrete anomalies in chiral gauge theories, J. High Energy Phys. 01 (2022) 112.
  12. A. Karasik, K. Önder, and D. Tong, Chiral gauge dynamics: Candidates for non-supersymmetric dualities, J. High Energy Phys. 11 (2022) 122.
  13. T. Appelquist, A. G. Cohen, M. Schmaltz, and R. Shrock, New constraints on chiral gauge theories, Phys. Lett. B 459, 235 (1999).
  14. T. Appelquist, Z. y. Duan, and F. Sannino, Phases of chiral gauge theories, Phys. Rev. D 61, 125009 (2000).
  15. S. Dimopoulos, S. Raby, and L. Susskind, Light composite fermions, Nucl. Phys. B173, 208 (1980).
  16. S. Bolognesi, K. Konishi, and A. Luzio, Strong anomaly and phases of chiral gauge theories, J. High Energy Phys. 08 (2021) 028.
  17. S. Bolognesi, K. Konishi, and A. Luzio, Anomalies and phases of strongly coupled chiral gauge theories: Recent developments, Int. J. Mod. Phys. A 37, 2230014 (2022); The Z2 anomaly in some chiral gauge theories, J. High Energy Phys. 08 (2023) 125.
  18. C. Csáki, H. Murayama, and O. Telem, More exact results on chiral gauge theories: The case of the symmetric tensor, Phys. Rev. D 105, 045007 (2022).
  19. H. Collins, A. K. Grant, and H. Georgi, Dynamically broken topcolor at large N, arXiv:hep-ph/9907477]; W. A. Bardeen, C. T. Hill, and D. U. Jungnickel, Chiral hierarchies, compositeness and the renormalization group, Phys. Rev. D 49, 1437 (1994).
  20. W. A. Bardeen, C. T. Hill, and M. Lindner, Minimal dynamical symmetry breaking of the standard model, Phys. Rev. D 41, 1647 (1990); C. T. Hill, Topcolor: Top quark condensation in a gauge extension of the standard model, Phys. Lett. B 266, 419 (1991).
  21. C. T. Hill, A new-old approach to composite scalars with chiral fermion constituents, Nucl. Phys. B1011, 116788 (2025); Natural top quark condensation (a Redux), arXiv:2503.21518.
  22. B. A. Dobrescu and C. T. Hill, Electroweak symmetry breaking via top condensation seesaw, Phys. Rev. Lett. 81, 2634 (1998); R. S. Chivukula, B. A. Dobrescu, H. Georgi, and C. T. Hill, Top quark Seesaw theory of electroweak symmetry breaking, Phys. Rev. D 59, 075003 (1999); B. A. Dobrescu, Minimal composite Higgs model with light bosons, 63, 015004 (2001).
  23. S. Raby, S. Dimopoulos, and L. Susskind, Tumbling gauge theories, Nucl. Phys. B169, 373 (1980).
  24. A. Tumasyan et al. (CMS Collaboration), Inclusive nonresonant multilepton probes of new phenomena at s=13  TeV, Phys. Rev. D 105, 112007 (2022).
  25. G. Aad et al. (ATLAS Collaboration), Search for third-generation vector-like leptons in pp collisions at s=13  TeV with the ATLAS detector, J. High Energy Phys. 07 (2023) 118.
  26. P. N. Bhattiprolu and S. P. Martin, Prospects for vectorlike leptons at future proton-proton colliders, Phys. Rev. D 100, 015033 (2019).
  27. E. Bernreuther and B. A. Dobrescu, Vectorlike leptons and long-lived bosons at the LHC, J. High Energy Phys. 07 (2023) 079; V. Chekhovsky et al. (CMS Collaboration), Search for vector-like leptons with long-lived particle decays in the CMS muon system in proton-proton collisions at s=13  TeV, arXiv:2503.16699.
  28. H. Georgi, H. R. Quinn, and S. Weinberg, Hierarchy of interactions in unified gauge theories, Phys. Rev. Lett. 33, 451 (1974).
  29. G. ’t Hooft, Dimensional regularization and the renormalization group, Nucl. Phys. B61, 455 (1973).
  30. J. C. Collins and A. J. Macfarlane, New methods for the renormalization group, Phys. Rev. D 10, 1201 (1974).
  31. R. N. Mohapatra and J. C. Pati, A natural left-right symmetry, Phys. Rev. D 11, 2558 (1975).
  32. M. E. Machacek and M. T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 1. Wave function renormalization, Nucl. Phys. B222, 83 (1983); Two loop renormalization group equations in a general quantum field theory. 2. Yukawa couplings, B236, 221 (1984).
  33. I. Jack and H. Osborn, General background field calculations with fermion fields, Nucl. Phys. B249, 472 (1985).
  34. A. G. M. Pickering, J. A. Gracey, and D. R. T. Jones, Three loop gauge beta function for the most general single gauge coupling theory, Phys. Lett. B 510, 347 (2001); 535, 377(E) (2002).
  35. A. Bednyakov and A. Pikelner, Four-loop gauge and three-loop Yukawa beta functions in a general renormalizable theory, Phys. Rev. Lett. 127, 041801 (2021).
  36. F. Staub, sarah 4: A tool for (not only SUSY) model builders, Comput. Phys. Commun. 185, 1773 (2014).
  37. A. E. Thomsen, Introducing rgbeta: A mathematica package for the evaluation of renormalization group β-functions, Eur. Phys. J. C 81, 408 (2021).
  38. B. A. Kniehl, A. F. Pikelner, and O. L. Veretin, mr: A C++ library for the matching and running of the standard model parameters, Comput. Phys. Commun. 206, 84 (2016).
  39. G. Huang and S. Zhou, Precise values of running quark and lepton masses in the standard model, Phys. Rev. D 103, 016010 (2021).
  40. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  41. M. J. Dolan, T. P. Dutka, and R. R. Volkas, Lowering the scale of Pati-Salam breaking through seesaw mixing, J. High Energy Phys. 05 (2021) 199.
  42. G. Valencia and S. Willenbrock, Quark—lepton unification and rare meson decays, Phys. Rev. D 50, 6843 (1994).
  43. L. Calibbi, A. Crivellin, and T. Li, Model of vector leptoquarks in view of the B-physics anomalies, Phys. Rev. D 98, 115002 (2018); S. Iguro, J. Kawamura, S. Okawa, and Y. Omura, TeV-scale vector leptoquark from Pati-Salam unification with vectorlike families, 104, 075008 (2021); Importance of vector leptoquark-scalar box diagrams in Pati-Salam unification with vectorlike families, J. High Energy Phys. 07 (2022) 022.
  44. F. Jegerlehner, Electroweak effective couplings for future precision experiments, Nuovo Cimento Soc. Ital. Fis. 34C, 31 (2011).
  45. C. Giunti, C. W. Kim, and U. W. Lee, Running coupling constants and grand unification models, Mod. Phys. Lett. A 06, 1745 (1991).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation